UNIFIED ENGINEERING
Fall 2003
Ian A. Waitz
Problem T8 (Unified Thermodynamics)
R=287 J/kg-K, cp=1003.5 J/kg-K, and cv = 716.5 J/kg-K. (MO# 5)
Below is a schematic diagram of a rocket engine cycle called an expander cycle. The cold
liquid propellants are pumped through the walls of the rocket nozzle to cool them. In doing
so, they gain energy and turn into gases. Some of the energy in these propellant gases is
then extracted in a turbine. The turbine is connected by a shaft to the liquid propellant
pump. After passing through the turbine, the propellant gases flow to the combustion
chamber where they are ultimately responsible for producing the heat at the walls of the
rocket nozzle. So it is a little like pulling yourself up by your bootstraps. As you might
expect, the design of a device like this depends on a careful analysis of the thermodynamics,
fluid mechanics and structural/material behavior.
Fuel
Turbopump
Turbopump
Oxidizer
To simplify the problem, we will consider only one of the propellants and assume that it is
always in gaseous form and behaves as an ideal gas with constant specific heats. Assume
R=260 J/kg-K, cp= 2800 J/kg-K, and cv = 2540 J/kg-K. (LO #4)
a) The cold propellant enters the pump at p = 1MPa, T = 200K and c = 50 m/s. The
flow rate is 100 kg/s. The flow leaves the pump at p = 5MPa and c = 50 m/s.
Assuming the pump behaves adiabatically and quasi-statically, what are the
conditions at the pump exit? How much shaft work and flow work were done by
propellant during the pumping process?
b) Assume that 1300 kJ/kg are absorbed by the gas as it passes along the walls of the
rocket nozzle. At entrance to the turbine, it is now flowing at c=100 m/s and
remains at p = 5MPa. What are the thermodynamic conditions at this point of the
engine. How much shaft work and flow work were done by the propellant during
the heating process?
c) Assuming the turbine behaves quasi-statically and adiabatically, what are the
conditions at the exit of the turbine assuming the velocity is c = 120m/s? How
much shaft work and flow work were done by the propellant in the turbine?